The module is called Sybase::DBlib (CASE MATTERS!!!).
I know nothing about Sybase::DBlib , but if dbsqlexec is printing errors to STDOUT (if on the screen means STDOUT ), you should try something like (untested):

my $err = "";
{
    require IO::String;
    local *main::STDOUT = $err = IO::String->new;
    $tcm->dbsqlexec || die "Error in dbsqlexec";
}
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now $err contains whatever dbsqlexec printed to STDOUT.

update: A better idea is to use select, as in (also untested):

my $err = "";
{
    my $orig = select IO::String->new(\$err);
    $tcm->dbsqlexec || die "Error in dbsqlexec";
    select $orig;
}
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